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An improved PTAS for covering targets with mobile sensors 一种用于移动传感器覆盖目标的改进PTAS
IF 1 4区 数学
Journal of Combinatorial Optimization Pub Date : 2025-01-20 DOI: 10.1007/s10878-024-01253-4
Nonthaphat Wongwattanakij, Nattawut Phetmak, Chaiporn Jaikaeo, Jittat Fakcharoenphol
{"title":"An improved PTAS for covering targets with mobile sensors","authors":"Nonthaphat Wongwattanakij, Nattawut Phetmak, Chaiporn Jaikaeo, Jittat Fakcharoenphol","doi":"10.1007/s10878-024-01253-4","DOIUrl":"https://doi.org/10.1007/s10878-024-01253-4","url":null,"abstract":"<p>This paper considers a movement minimization problem for mobile sensors. Given a set of <i>n</i> point targets, the <i>k-Sink Minimum Movement Target Coverage Problem</i> is to schedule mobile sensors, initially located at <i>k</i> base stations, to cover all targets minimizing the total moving distance of the sensors. We present a polynomial-time approximation scheme for finding a <span>((1+epsilon ))</span> approximate solution running in time <span>(n^{O(1/epsilon )})</span> for this problem when <i>k</i>, the number of base stations, is constant. Our algorithm improves the running time exponentially from the previous work that runs in time <span>(n^{O(1/epsilon ^2)})</span>, without any target distribution assumption. To devise a faster algorithm, we prove a stronger bound on the number of sensors in any unit area in the optimal solution and employ a more refined dynamic programming algorithm whose complexity depends only on the width of the problem.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"74 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Covering spaces of symplectic toric orbifolds 复盖辛环轨道的空间
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-01-20 DOI: 10.1007/s10455-025-09984-1
Paweł Raźny, Nikolay Sheshko
{"title":"Covering spaces of symplectic toric orbifolds","authors":"Paweł Raźny,&nbsp;Nikolay Sheshko","doi":"10.1007/s10455-025-09984-1","DOIUrl":"10.1007/s10455-025-09984-1","url":null,"abstract":"<div><p>In this article we study covering spaces of symplectic toric orbifolds and symplectic toric orbifold bundles. In particular, we show that all symplectic toric orbifold coverings are quotients of some symplectic toric orbifold by a finite subgroup of a torus. We then give a general description of the labeled polytope of a toric orbifold bundle in terms of the polytopes of the fiber and the base. Finally, we apply our findings to study the number of toric structures on products of labeled projective spaces.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"67 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142995368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Algebraic Version of the Poincare Construction 庞加莱构造的代数版本
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-01-20 DOI: 10.1134/S0016266324040063
Maria Stepanova
{"title":"An Algebraic Version of the Poincare Construction","authors":"Maria Stepanova","doi":"10.1134/S0016266324040063","DOIUrl":"10.1134/S0016266324040063","url":null,"abstract":"<p> The Poincare construction in CR geometry allows us to estimate the dimension of the stabilizer in the Lie algebra of infinitesimal holomorphic automorphisms of the germ of a CR manifold by the dimension of the stabilizer in the corresponding algebra of the model surface of this germ. We give a negative answer to the following natural question: is there an algebraic Poincare construction, i.e., is it true that the stabilizer in the Lie algebra of automorphisms of the germ of a CR manifold is isomorphic to a Lie subalgebra of the stabilizer in the algebra of its model surface? We also give a negative answer to the corresponding question for the whole automorphisms algebra. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 4","pages":"427 - 437"},"PeriodicalIF":0.6,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142995173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
1-Planar graphs with no 5-cycles are 5-degenerate
IF 4 2区 数学
Applied Mathematics and Computation Pub Date : 2025-01-20 DOI: 10.1016/j.amc.2025.129304
Qingqin Wu, Weifan Wang, Jiangxu Kong
{"title":"1-Planar graphs with no 5-cycles are 5-degenerate","authors":"Qingqin Wu, Weifan Wang, Jiangxu Kong","doi":"10.1016/j.amc.2025.129304","DOIUrl":"https://doi.org/10.1016/j.amc.2025.129304","url":null,"abstract":"A graph is 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. A graph is <ce:italic>k</ce:italic>-degenerate if each of its subgraphs contains a vertex of degree no greater than <ce:italic>k</ce:italic>. It was known that 1-planar graphs are 7-degenerate. In this paper, we show that every 1-planar graph without 5-cycles is 5-degenerate, which extends some known results on the 5-degeneracy of some 1-planar graphs.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"20 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fusing structural and temporal information in citation networks for identifying milestone works 融合引文网络中的结构和时间信息以识别里程碑作品
IF 7.8 1区 数学
Chaos Solitons & Fractals Pub Date : 2025-01-20 DOI: 10.1016/j.chaos.2025.116004
Yuhao Zhou, Faming Gong, Yanwei Wang, Ruijie Wang, An Zeng
{"title":"Fusing structural and temporal information in citation networks for identifying milestone works","authors":"Yuhao Zhou, Faming Gong, Yanwei Wang, Ruijie Wang, An Zeng","doi":"10.1016/j.chaos.2025.116004","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116004","url":null,"abstract":"The rapid proliferation of scientific and technological works has highlighted the necessity to effectively identify the significant achievements in more and more complex citation networks. Mainstream algorithms fall into two categories: structural information based algorithms with Citation and PageRank as the core; Temporal information based algorithms represented by the citation dynamic model and Relevance. This article conducts a detailed study of the relationship between these two categories to fill the gap in this area. We use the American Physical Society (APS) dataset, which includes 469,452 papers and 5,016,382 citations from 1893 to 2010. Our findings indicate that PageRank and Citation are statistically similar, both favoring older articles. However, Relevance excels in early forecasting, hence showing a weaker correlation with PageRank. Inspired by this, we introduce a new method called Structural-Temporal Rank (STRank). Validation experiments demonstrate that STRank excels in identifying milestone letters and predicting future impact, outperforming other methods in these tasks. This study introduces the idea of fusing structural and temporal information in designing ranking methods that could guide the future development of more efficient node identification algorithms in networks.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"33 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lack of Metric Projectivity, Injectivity, and Flatness for Modules (L_p) 缺少度量投射性、注入性和模块平整度 (L_p)
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-01-20 DOI: 10.1134/S0016266324040038
Norbert Nemesh
{"title":"Lack of Metric Projectivity, Injectivity, and Flatness for Modules (L_p)","authors":"Norbert Nemesh","doi":"10.1134/S0016266324040038","DOIUrl":"10.1134/S0016266324040038","url":null,"abstract":"<p> In this paper, we demonstrate that for a locally compact Hausdorff space <span>(S)</span> and a decomposable Borel measure <span>(mu)</span>, metric projectivity, injectivity, or flatness of the <span>(C_0(S))</span>-module <span>(L_p(S,mu))</span> implies that <span>(mu)</span> is purely atomic with at most one atom. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 4","pages":"371 - 383"},"PeriodicalIF":0.6,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142995178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Recognizing integrality of weighted rectangles partitions 加权矩形分区的完整性识别
IF 1 4区 数学
Journal of Combinatorial Optimization Pub Date : 2025-01-20 DOI: 10.1007/s10878-024-01252-5
Paul Deuker, Ulf Friedrich
{"title":"Recognizing integrality of weighted rectangles partitions","authors":"Paul Deuker, Ulf Friedrich","doi":"10.1007/s10878-024-01252-5","DOIUrl":"https://doi.org/10.1007/s10878-024-01252-5","url":null,"abstract":"<p>Given a grid of active and inactive pixels, the weighted rectangles partitioning (WRP) problem is to find a maximum-weight partition of the active pixels into rectangles. WRP is formulated as an integer programming problem and instances with an integral relaxation polyhedron are characterized by a balanced problem matrix. A complete characterization of these balanced instances is proved. In addition, computational results on balancedness recognition and on solving WRP are presented.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"31 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Degree and betweenness-based label propagation for community detection 基于度和间性标签传播的社群检测
IF 1 4区 数学
Journal of Combinatorial Optimization Pub Date : 2025-01-20 DOI: 10.1007/s10878-024-01254-3
Qiufen Ni, Jun Wang, Zhongzheng Tang
{"title":"Degree and betweenness-based label propagation for community detection","authors":"Qiufen Ni, Jun Wang, Zhongzheng Tang","doi":"10.1007/s10878-024-01254-3","DOIUrl":"https://doi.org/10.1007/s10878-024-01254-3","url":null,"abstract":"<p>Community detection, as a crucial network analysis technique, holds significant application value in uncovering the underlying organizational structure in complex networks. In this paper, we propose a degree and betweenness-based label propagation method for community detection (DBLPA). First, we calculate the importance of each node by combining node degree and betweenness centrality. A node <i>i</i> is considered as a core node in the network if its importance is maximal among its neighbor nodes. Next, layer-by-layer label propagation starts from core nodes. The first layer of nodes for label propagation consists of the first-order neighbors of all core nodes. In the first layer of label propagation, the labels of core nodes are first propagated to the non-common neighbor nodes between core nodes, and then to the common neighbor nodes between core nodes. At the same time, the <i>flag</i> parameter is set to record the changing times of a node’s label, which is helpful to calibrate the node’s labels during the label propagation. It effectively improves the misclassification in the process of label propagation. We test the DBLPA on four real network datasets and nine synthetic network datasets, and the experimental results show that the DBLPA can effectively improve the accuracy of community detection.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"9 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Social media actors: perception and optimization of influence across different types 社交媒体参与者：感知和优化不同类型的影响力
IF 1 4区 数学
Journal of Combinatorial Optimization Pub Date : 2025-01-20 DOI: 10.1007/s10878-024-01238-3
Alexander A. Kharlamov, Aleksey N. Raskhodchikov, Maria Pilgun
{"title":"Social media actors: perception and optimization of influence across different types","authors":"Alexander A. Kharlamov, Aleksey N. Raskhodchikov, Maria Pilgun","doi":"10.1007/s10878-024-01238-3","DOIUrl":"https://doi.org/10.1007/s10878-024-01238-3","url":null,"abstract":"<p>The paper deals with the analysis of the communicative behavior of various types of actors, speech perception and optimization of influence based on social media data and is an extended version of the report presented at CSoNet 2020 and published based on the deliverables of the conference. The paper proposes an improved methodology that is tested on the new material of conflicts regarding urban planning. The research was conducted on the material of social media concerning the construction of the South-East Chord in Moscow (Russia). The study involved a cross-disciplinary approach using neural network technologies, complex networks analysis. The dataset included social networks, microblogs, forums, blogs, videos, reviews. This paper presents the semantic model for the influence maximization analysis in social networks using neural network technologies, also proposed a variant of analyzing the situation with individual and collective actors, multiple opinion leaders, with a dynamic transformation of the hierarchy and ratings according to various parameters.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"107 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Diffusion Mechanism in Hamiltonian Systems 关于哈密顿系统中的扩散机制
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-01-20 DOI: 10.1134/S0016266324040026
Valery Kozlov
{"title":"On the Diffusion Mechanism in Hamiltonian Systems","authors":"Valery Kozlov","doi":"10.1134/S0016266324040026","DOIUrl":"10.1134/S0016266324040026","url":null,"abstract":"<p> The diffusion mechanism in Hamiltonian systems, close to completely integrable, is usually connected with the existence of the so-called “transition chains”. In this case slow diffusion occurs in a neighborhood of intersecting separatrices of hyperbolic periodic solutions (or, more generally, lower-dimensional invariant tori) of the perturbed system. In this note we discuss another diffusion mechanism that uses destruction of invariant tori of the unperturbed system with an almost resonant set of frequencies. We demonstrate this mechanism on a particular isoenergetically nondegenerate Hamiltonian system with three degrees of freedom. The same phenomenon also occurs for general higher-dimensional Hamiltonian systems. Drift of slow variables is shown using analysis of integrals of quasi-periodic functions of the time variable (possibly unbounded) with zero mean value. In addition, the proof uses the conditions of topological transitivity for cylindrical cascades. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 4","pages":"362 - 370"},"PeriodicalIF":0.6,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142995176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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